Question: $f(t) = 3t-3(g(t))$ $g(t) = -t^{2}+2t$ $ g(f(-2)) = {?} $
Solution: First, let's solve for the value of the inner function, $f(-2)$ . Then we'll know what to plug into the outer function. $f(-2) = (3)(-2)-3(g(-2))$ To solve for the value of $f$ , we need to solve for the value of $g(-2)$ $g(-2) = -(-2)^{2}+(2)(-2)$ $g(-2) = -8$ That means $f(-2) = (3)(-2)+(-3)(-8)$ $f(-2) = 18$ Now we know that $f(-2) = 18$ . Let's solve for $g(f(-2))$ , which is $g(18)$ $g(18) = -18^{2}+(2)(18)$ $g(18) = -288$